Multiply fractions by whole numbers
Multiplying a fraction by a whole number is like adding that fraction to itself multiple times! It's a shortcut for repeated addition.
Concept
Multiplying fractions by whole numbers is repeated addition! šÆ **Understanding the Concept:** **What does 4 Ć 1/3 mean?** It means: 1/3 + 1/3 + 1/3 + 1/3 Visual: [Four 1/3 pieces shaded] Adding: 1/3 + 1/3 + 1/3 + 1/3 = 4/3 So: 4 Ć 1/3 = 4/3 = 1 1/3 š” **The Rule:** To multiply a whole number by a fraction: Multiply the whole number by the NUMERATOR Keep the DENOMINATOR the same **Example 1:** 3 Ć 2/5 = ? 3 Ć 2/5 = (3 Ć 2)/5 = 6/5 = 1 1/5 **Example 2:** 5 Ć 3/4 = ? 5 Ć 3/4 = (5 Ć 3)/4 = 15/4 = 3 3/4 š **Step-by-Step:** **Solve: 6 Ć 2/3** Step 1: Write the whole number over 1: 6/1 Ć 2/3 Step 2: Multiply numerators: 6 Ć 2 = 12 Step 3: Multiply denominators: 1 Ć 3 = 3 Step 4: Write answer: 12/3 Step 5: Simplify: 12/3 = 4 š **Number Line Model:** 3 Ć 1/4 on a number line: 0----1/4----2/4----3/4----1 ā ā ā 1st 2nd 3rd Three jumps of 1/4 = 3/4 šØ **Real-World Thinking:** **Problem:** You have 4 friends. Each friend eats 2/5 of a pizza. How much pizza total? 4 Ć 2/5 = (4 Ć 2)/5 = 8/5 = 1 3/5 pizzas **Problem:** A recipe calls for 3/4 cup flour. You want to make 5 batches. How much flour? 5 Ć 3/4 = 15/4 = 3 3/4 cups š **Why Multiply the Numerator?** When you have 3 groups of 2/5, you have: ā¢ 2/5 + 2/5 + 2/5 = (2+2+2)/5 = 6/5 The denominator (5) stays the same because the piece size doesn't change!
Try it
Practice multiplying fractions by whole numbers! š **Multiply:** 1. 2 Ć 1/4 = ? 2. 3 Ć 1/5 = ? 3. 4 Ć 2/3 = ? 4. 5 Ć 3/4 = ? š¢ **Solve and Simplify:** 5. 6 Ć 1/2 = ? 6. 3 Ć 4/5 = ? 7. 2 Ć 5/6 = ? 8. 4 Ć 3/8 = ? šÆ **Convert to Mixed Numbers:** 9. 5 Ć 2/3 = ? (write as a mixed number) 10. 7 Ć 3/4 = ? (write as a mixed number) š **Word Problems:** 11. Each student needs 2/5 yard of ribbon. If there are 8 students, how much ribbon is needed total? 12. A recipe for one smoothie uses 3/4 cup of yogurt. How much yogurt is needed for 6 smoothies? 13. Each lap around the track is 1/4 mile. If you run 12 laps, how many miles did you run? šŖ **Challenge:** 14. If 4 Ć ?/5 = 8/5, what fraction goes in the box? 15. Which is greater: 3 Ć 5/6 or 4 Ć 3/4? Show your work. 16. 10 Ć 2/5 = ? (Think: Can you simplify before multiplying?) šØ **Draw It:** 17. Draw a model showing 3 Ć 2/4 = 6/4 = 1 2/4 = 1 1/2